domain of f(x) is x doesn't equal -3 range of f^-1(x) is y doesn't equal -3
range of f(x) is y doesn't equal -1 domain of f^-1(x) is x doesn't equal -1
to find inverse: solve x = (2 – y) / (3 + y) for y
x(3 +y) = 2 – y 3x + xy = 2 – y y + xy = 2 – 3x y(1 + x) = 2 – 3x y = f^-1(x) = (2 – 3x) / (1 + x) domain of f^-1(x): x doesn't equal -1 (range of f(x): y <>-1) range of f^-1(x): y doesn't equal -3 (domain of f(x): x <>-3)
July 1st, 2008 at 9:16 am
f inverse = interchange x and y and solve x in terms of y
domain = all real numbers
July 1st, 2008 at 9:16 am
domain of f(x) is x doesn't equal -3
range of f^-1(x) is y doesn't equal -3
range of f(x) is y doesn't equal -1
domain of f^-1(x) is x doesn't equal -1
to find inverse: solve x = (2 – y) / (3 + y) for y
x(3 +y) = 2 – y
3x + xy = 2 – y
y + xy = 2 – 3x
y(1 + x) = 2 – 3x
y = f^-1(x) = (2 – 3x) / (1 + x)
domain of f^-1(x): x doesn't equal -1 (range of f(x): y <>-1)
range of f^-1(x): y doesn't equal -3 (domain of f(x): x <>-3)
check: find f(-2) = (2 – -2) / (3 + -2) = 4/1 = 4
now find f^-1(4) = (2 – 3(4)) / (1 + 4) = -10 / 5 = -2
so (-2,4) on f(x); (4, -2) on f^-1(x) check
July 1st, 2008 at 9:16 am
(2-y)/(3+y)=x
2-y=3x+xy
xy+y=2-3x
y(x+1)=2-3x
y=(2-3x)/(x+1)
dom f=x <>-3, dom f^-1=x<>-1, where '<>'means "not equal to"
January 26th, 2012 at 7:32 pm
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